This general relativistic Hamilton-Jacobi equation
becomes a scalar wave equation via the transformation to eliminate the squared first derivative, i.
One can check directly that the coordinate transformations given by equation (19) takes the free Hamilton-Jacobi equation ([delta]S/[delta]t)[sup.
which is the Hamilton-Jacobi equation (27) for m=0.
In a series of papers [3, 4, 5], we derived a Schrodinger-like scalar wave equation from the general relativistic Hamilton-Jacobi equation
via a tranformation that utilizes the total angular momentum of the gravitationally bound system instead of an angular momentum proportional to Planck's constant.
When the above expression for the Weyl scalar curvature (Bohm's quantum potential given in terms of the ensemble density) is inserted into the Hamilton-Jacobi equation
, in conjunction with the continuity equation, for a momentum given by [p.
First he looks at connections between Schrodinger and Hamilton-Jacobi equations
in the case of stationary atomic and molecular systems, then at connections between Klein-Gordon and relativistic Hamilton-Jacobi equations
for systems composed of electromagnetic fields and particles.
There are other applications of asymmetric metrics both in pure and applied mathematics; for example, asymmetric metric spaces have recently been studied with questions of existence and uniqueness of Hamilton-Jacobi equations
 in mind.
from which the Hamilton-Jacobi equations
are derived, Hamiltonian vector field of [H.
The topics include a level set method for the numerical simulation of damage evolution, some nonlinear problems involving non-local diffusions, radar imaging, the multiscale analysis of density function theory, asymptotic solutions of Hamilton-Jacobi equations
for large time and related topics, second-order partial differential equations and deterministic games, order-value optimization and new applications, visibility and invisibility, and the life and work of Leonhard Euler.
in Hilbert Spaces (joint with G.
Subjects featured include kinetic formulations of nonlinear PDEs, constrained Hamilton-Jacobi equations
, nonlinear Schrodinger equations, quasiminimal sets for Hausdorff measures, Schrodinger flows into Kahler manifolds, and parabolic obstacle problems with applications to finance.
Other topics include homogenization of stochastic Hamilton-Jacobi equations
, general relative entropy in a nonlinear McKendrick model, pointwise Fourier inversion in analysis and geometry, and a class of one-dimensional Markov processes with continuous paths.